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The **implicitdiff** command can be used to find derivatives of implicitly defined functions. The syntax is as follows

> implicitdiff(f,y,x);where

> f:=x^2*y^2+y^3;

> implicitdiff(f,y,x);

> g:=x^2+y^3=1;

> implicitdiff(g,y,x);Second derivatives can also be taken with

> implicitdiff(g,y,x,x);Maple also has a command for plotting implicitly defined functions. It is in the package

> with(plots);

> implicitplot(x^2-y^2=1,x=-3..3,y=3..3);

- 1.
- The graph of the equation
*x*-^{2}*xy*+*y*=9 is a rotated ellipse.^{2}- a.
- Plot the graph of the curve.
- b.
- Using implicit differentiation find
*y*'. - c.
- Show that the tangents to this curve at the two points where it intersects the x-axis are parallel.
- d.
- Is that true for the tangents to this ellipse at any pair of points obtained by intersecting the ellipse with a line passing through the origin? Justify your answer.

- 2.
- Consider the following implicitly defined functions
*y*. Find the equations of the line tangents at the given points

- 3.
- A lighthouse is one mile out to the sea from a stretch of straight shore. Its beacon rotates three times per minute. Let A be the point on the shore nearest the lighthouse and B a point on the shore three miles far from A. How fast does the spot of light from the beacon travel (along the shore AB) as it passes point B?

**DUE DATE: FEBRUARY 15 (in class).**

2/10/1999